Question

If the coefficient of variation and standard deviation of a distribution are $50\% $ and $20$ respectively, then its mean is
A) 40
B) 30
C) 20
D) None of these

Answer 1

Hint: In this question the coefficient of variation and standard deviation of distribution are given, then in order to find its mean we will use the simple formula of coefficient of variation which is given by
Coefficient of variation $ = \dfrac{\sigma }{{\overline x }} \times 100$
Where
$\overline x $ is the mean distribution.
and $\sigma $ is the standard deviation.

Complete step-by-step answer:
Given that coefficient of variation $ = 50\% $
And standard deviation $ = 20$
Let the mean of distribution = $\overline x $
We know if a distribution having mean $\overline x $ and standard deviation $\sigma $
Then coefficient of variation $ = \dfrac{\sigma }{{\overline x }} \times 100$
By substituting the values, we have
$
   \Rightarrow 50 = \dfrac{{20}}{{\overline x }} \times 100 \\
   \Rightarrow \overline x = \dfrac{{20 \times 100}}{{50}} \\
   \Rightarrow \overline x = 40 \\
 $
Hence required mean is 40 and the correct answer is Option “A”.

Note: In order to solve problems related to standard deviation, mean deviation, co- variance etc. remember all the formulas. The concept behind them is simple such as mean can be termed as average of the given data or quantities. Similarly the standard deviation can be defined as the quantity expressing how many members of a group differ from the mean value of that group.